Sensitivity analysis method for model with correlated inputs and multivariate output and its application to aircraft structure

• Published in: Computer methods in applied mechanics and engineering Vol. 355; pp. 373 - 404
• Main Authors: Xu, Liyang, Lu, Zhenzhou, Li, Luyi, Shi, Yan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2019; Elsevier BV
• Subjects: Aircraft; Aircraft structures; Correlated inputs; Correlation analysis; Covariance; Data envelopment analysis; Multivariate analysis; Multivariate output; Projection; Sensitivity analysis; Variance; Vector projection; Correlated inputs; Multivariate output; Vector projection; Sensitivity analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.06.015

Traditional sensitivity analysis methods for the model with correlated inputs and univariate output fail to provide satisfactory results for multivariate output. In this work, we first establish a reasonable contribution classification for the univariate output with the correlated input. Then the covariance decomposition method is extended to the case of correlated inputs as a reference, and the vector projection sensitivity index is extended to aggregate the correlated and uncorrelated contributions of the input to multiple outputs. The definition of the new sensitivity index is based on the vector projection, which can take into account both uncertainties and correlations among multiple outputs by projecting the conditional variance vector (built by the full marginal variance contributions) on the unconditional variance vector (built by unconditional variance magnitudes and correlation of the multiple outputs). The mathematical properties of the extended vector projection sensitivity index are discussed and its relations with other existing sensitivity indices are highlighted. Two numerical examples and two engineering examples about an aircraft structure are employed to illustrate the validity and potential benefits of the extended vector projection sensitivity index. •Correct classification of contribution of correlated input in original method.•Extend covariance decomposition method to the case of correlated inputs.•Extend vector projection method to the case of correlated inputs and outputs.•Highlight relationships between proposed methods with other existing indices.•Aircraft models are employed to illustrate validity and potential benefits of index.